where \(k\)  is the number of clusters, and \(N\)  is the total number of observations (i.e., data points), \(\text{SS}_W\)  is the overall within-cluster variance and, \(\text{SS}_M\)  is the overall between-cluster variance.
Note that a higher value is associated with dense and well-distributed clusters.
Finally, we employ the Davies-Bouldin Index (DBI) [1]} denoted by
\(\text{DBI} = \frac{1}{k}\sum _i^k \max _{j \ne i}\left(\frac{s_i + s_j}{d_{ij}}\right),\) 
